Answers
CHAPTER 1 Quadratic Functions and
Equations in One Variable
Self Practice 1.1a
1. (a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
2. (a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Yes
No because its power is not a whole number
No because there are two variables, x and y
Yes
No because the highest power is three
No because its power is not a whole number
No because its power is not a whole number
Yes
Yes
a = 2,
b = –5,
c=1
a = 1,
b = –2,
c=0
a = 2,
b = 0,
c=1
1
a=– ,
b = 4,
c=0
2
a = –2,
b = –1,
c=1
a = 4,
b = 0,
c=0
3
c = –4
a = 1,
b=
2
1
b = 0,
c = –2
a= ,
3
a = 2,
b = –6
c=0
Self Practice 1.1b
1. (a)
2. (a)
(b)
3. (a)
(b)
(c)
(d)
(b)
a  0, minimum point
a  0, maximum point
Minimum point (4, –15), x = 4
Maximum point (3, 13.5), x = 3
Maximum point (–2, 4), x = –2
Minimum point (2, –2), x = 2
(c) x = – 1 is a root,
3
(d) x = 2 is not a root,
3. (a)
(b)
(c)
4. (a)
(c)
x = –2 is not a root
2
x = is a root
3
x = – 4 and x = 1 are roots, x = 2 is not a root
x = 3 and x = 5 are roots, x = –3 is not a root
x = –2 and x = 4 are roots, x = 2 is not a root
x = 1 is not a root
(b) x = –3 is a root
x = 15 is not a root (d) x = 5 is a root
Self Practice 1.1f
1. (a) x = 5, x = –2
(c) x = 2, x = 1
3
3
(e) x = –3, x =
2
(g) x = – 7, x = 2
3
(i) x = –2, x = 2
2. (a) m2 + 2m – 3 = 0;
(b) x = 2, x = 8
(d) x = –6, x = 2
5
(f) x = – , x = 2
4
(h) x = 0, x = 5
(c)
+ 2y – 24 = 0;
(d) a2 – 6a + 5 = 0;
(e) k2 + 2k – 8 = 0;
(f) 2h2 – 7h + 6 = 0;
m = –3,
1
p=2,
y = 4,
a = 5,
k = 2,
h = 2,
(g) h2 – 3h – 10 = 0;
(h) 4x2 – 7x + 3 = 0;
(i) r2 – 6r + 9 = 0;
h = –2,
3
x= ,
4
r=3
(b) 2p2 – 11p + 5 = 0;
y2
Self Practice 1.1c
1. (a)
1. (a) x = –0.35, x = 2
(b) x = –4,
x=5
2. (a) x = 3 is a root,
(b) x = 1 is a root,
f (x)
(3, 14)
14
–4
O
x
3
5
–3 O
(b)
(b)
f (x)
9
O
(c)
–2
f (x)
(c)
O
2
x
f (x)
40
2
2
–2
–4
(2, 9)
1
x
4
x
3
f (x)
16
(b) x2 + 25x – 150 = 0
Self Practice 1.1e
y = –6
a=1
k = –4
3
h=
2
h=5
x=1
2. (a)
f (x)
Self Practice 1.1d
1. (a) A = x2 + 25x + 100
2. p2 + 4p – 48 = 0
p=5
Self Practice 1.1g
–24
1. (a) 5
(b) –3
(c) 4
2. 0  p  4
Function f(x) has a wider curve, thus p  4.
For graph in the shape of , a  0, thus p  0
3. (a) k = –1
(b) h = 5
(c) f (x) = x2 – 6x – 5
m=1
O
5
x
O
–2
x
(2, –2)
f (x)
(d)
8
x = 2 is a root
1
x = is not a root
2
–2
O
2
x
Saiz sebenar
293
Self Practice 1.1h
1. (a) A = 5x2 + 20x
2. Yes
(b) RM8 000
1. (a) Yes
(d) No
2. (a) x = 2
(c) No
(f) Yes
(b) x = 3
(b) Yes
(e) Yes
1
3. (a) x = – 1 , x =
2
2
(b) x = –9, x = 9
(c) y = 0, y = 4
(d) x = –1, x = –2
5
(e) x = –2, x =
2
(f) x = 6, x = –2
(g) m = 1, m = – 4
5
(h) p = 4, p =
2
(i) k = 7, k = –2
(j) h = 2, h = –2
3
(k) x = 5, x =
2
4. p = 7
5. m = 6, m = 4
6. (3, –4)
7. (4, 23)
8. (a) A (0, –5)
(b) x = 3
(c) B (6, –5)
(d) (3, 4)
9. (a) c = 6
(b) m = –2
(c) a = 2
(d) n = –2
(ii) k = 5
(iii) a = 3
10. (a) (i) h = 1
(b) x = 3
(c) P(3, –12)
11. (a) A = x2 – 3x – 4
(b) length = 8 cm, width = 3 cm
12. 20 cm
13. (a) A = x2 + 27x + 180 (b) x = 8
(c) enough
14. (a) A = x2 – 5x – 4
(b) x = 7
(c) 38 m
CHAPTER 2 Number Bases
Self Practice 2.1a
Saiz
1. Accept pupil’s correct answers.
2. 461, 371, 829
3. (a) 234
(b) 234, 336
(c) 234, 336, 673
sebenar
(d) 234, 336, 673, 281
294
4. (a) 24
(b) 52
(d) 61
(e) 32
(g) 42
(h) 83
0
(j) 5
5. (a) 4
(b) 10
(d) 72
(e) 54
(g) 8
(h) 448
(j) 4
6. (a) 15
(b) 277
(d) 278
(e) 193
(g) 38
(h) 655
(j) 43
7. (a) p = 3, q = 22
(b) p = 2, q = 7
(c) p = 4, q = 3
8. 651
9. (a) 1102, 1112, 11012, 11102
(b) 1124, 1324, 2314, 11234
(c) 1245, 2315, 2415, 3245
10. (a) 12134, 899, 1111012
(b) 3135, 738, 1234
(c) 2536, 1617, 2223
11. 315
(c) 71
(f) 91
(i) 62
(c) 3
(f) 2 058
(i) 12
(c) 53
(f) 15
(i) 191
Self Practice 2.1b
1. (a) 1111011102
(d) 7568
2. (a) 10223
(d) 2516
3. 10103
4. (a) 758
(d) 528
5. (a) 1000112
(c) 1011112
(e) 1100111012
(b)
(e)
(b)
(e)
132324
6089
245
2518
(c) 34345
(b)
(e)
(b)
(d)
(f)
168
(c) 3678
708
(f) 7258
10010102
10100011112
101000112
(c) 1000010012
(f) 100124
Self Practice 2.1c
1. (a) 1012
(d) 12203
(g) 11035
(j) 2136
(m) 20208
(p) 65539
2. (a) 11012
(d) 1213
(g) 3235
(j) 11036
(m) 7468
(p) 14439
(b)
(e)
(h)
(k)
(n)
1110012
234
40025
4527
7358
(c)
(f)
(i)
(l)
(o)
11013
31104
5136
11137
2119
(b)
(e)
(h)
(k)
(n)
1102
104
11415
54537
42018
(c)
(f)
(i)
(l)
(o)
12223
3024
34136
63137
6459
Self Practice 2.1d
1.
2.
3.
4.
x = 557
(a) 168
Puan Aminah
1600 m2
(b) 1345
2. (a) True
(e) True
1. (a) 2405, 2415, 2425
(b) 1102, 1112, 10002
(c) 317, 327, 337
2. 32
3. (a) 7168
(b) 111101112
4. (a) 111100012 (b)
(c) 4637
(d)
5. (a) 101012
(b)
6. (a) True
(b)
7. 269
8. 39
9. y = 105
10. (a) 658, 1101102
(b) 1768, 10035
11. 1325
12. 558
13. 427
(c) False
(g) False
(d) False
(h) True
Self Practice 3.1d
14315
3618
4427
True
(c) 569
(c) False
CHAPTER 3 Logical Reasoning
Self Practice 3.1a
1. (a) Not a statement. Because the truth value cannot
be determined.
(b) A statement. Because it is true.
(c) Not a statement. Because the truth value cannot
be determined.
(d) A statement. Because it is true.
(e) Not a statement. Because the truth value cannot
be determined.
2. (a) 40  23 + 9
(b) {3}  {3, 6, 9}
(c) 1 × 10 = 5
4 3 6
(d) x2 + 3  (x + 3)2
(e) 3√ 27 + 9 = 12
3. (a) False
(b) False
(d) True
(e) True
(c) False
819 is not a multiple of 9.
A kite does not have two axes of symmetry.
A cone does not have one curved surface.
Two parallel lines do not have the
same gradient.
5. Not all quadratic equations have two
equal roots.
1. (a) If x = 3, then x4 = 81.
(b) If ax3 + bx2 + cx + d = 0 is a cubic equation, then
a ≠ 0.
(c) If n – 5  2n, then n  –5.
m
(d) If n  1, then m2  n2.
2. (a) Antecedent: x is an even number.
Consequent: x2 is an even number.
(b) Antecedent: set K = φ.
Consequent: n(K) = 0.
(c) Antecedent: x is a whole number.
Consequent: 2x is an even number.
(d) Antecedent: A straight line AB is a tangent to
a circle P.
Consequent: A straight line AB touches the circle
P at one point only.
3. (a) k is a perfect square if and only if √k is a whole
number.
(b) P  Q = P if and only if P  Q.
(c) pq = 1 if and only if p = q–1 and q = p–1.
(d) k2 = 4 if and only if (k + 2)(k – 2) = 0.
4. (a) If PQR is a regular polygon, then PQ = QR = PR.
If PQ = QR = PR, then PQR is a regular polygon.
(b) If m
n is an improper fraction, then m  n.
If m  n, then m
n is an improper fraction.
(c) If 9 is the y-intercept of a straight line y = mx + c,
then c = 9.
If c = 9, then 9 is the y-intercept of a straight line
y = mx + c.
(d) If f (x) = ax2 + bx + c has a maximum point, then
a  0.
If a  0, then f (x) = ax2 + bx + c has a maximum
point.
Self Practice 3.1e
Self Practice 3.1b
1.
2.
3.
4.
(b) False
(f) True
False
True
False
False
True
Self Practice 3.1c
1. (a) 2 or 3 is a prime factor of the number 6.
(b) A cone has one vertex and one plane.
(c) A rhombus and a trapezium are parallelograms.
1. (a) Converse:
If x  –1, then x + 3  2.
Inverse:
If x + 3  2, then x  –1.
Contrapositive: If x  –1, then x + 3  2.
(b) Converse:
If k = 3 or k = –4, then
(k – 3)(k + 4) = 0.
Inverse:
If (k – 3)(k + 4) ≠ 0, then k ≠ 3 or
k ≠ –4.
Contrapositive: If k ≠ 3 or k ≠ – 4, then
(k – 3)(k + 4) ≠ 0.
(c) Converse:
If AB is parallel to CD, then
ABCD is a parallelogram.
Inverse:
If ABCD is not a parallelogram,
then AB is not parallel to CD.
Contrapositive: If AB is not parallel to Saiz
CD, then
sebenar
ABCD is not a parallelogram.
295
2. (a)
Implication: If 2 and 5 are the factors
of 10, then 2 × 5 is 10.
Converse: If 2 × 5 is 10, then 2 and 5
are the factors of 10.
Inverse: If 2 and 5 are not the factors
of 10, then 2 × 5 is not 10.
Contrapositive: If 2 × 5 is not 10, then
2 and 5 are not the factors of 10.
True
(b) Implication: If 4 is a root of x2 – 16 = 0,
then 4 is not a root of
(x + 4)(x – 4) = 0.
Converse: If 4 is not a root of
(x + 4) (x – 4) = 0, then 4 is a root of
x2 – 16 = 0.
Inverse: If 4 is not a root of x2 – 16 = 0,
then 4 is a root of (x + 4)(x – 4) = 0.
Contrapositive: If 4 is a root of
(x + 4)(x – 4) = 0, then 4 is not a root
of x2 – 16 = 0.
False
(c)
True
Implication: If a rectangle has four
axes of symmetry, then the rectangle
has four sides.
Converse: If a rectangle has four
sides, then the rectangle has four axes
of symmetry.
Inverse: If a rectangle does not have
four axes of symmetry, then the
rectangle does not have four sides.
Contrapositive: If a rectangle does
not have four sides, then the rectangle
does not have four axes of symmetry.
(d) Implication: If 55 + 55 = 4 × 5, then
666 + 666 = 6 × 6
Converse: If 666 + 666 = 6 × 6,
then 55 + 55 = 4 × 5.
Inverse: If 55 + 55 ≠ 4 × 5, then
666 + 666 ≠ 6 × 6.
Contrapositive: If 666 + 666 ≠ 6 × 6,
then 55 + 55 ≠ 4 × 5.
True
True
True
True
True
False
False
False
True
True
True
True
True
Self Practice 3.1f
Saiz
1. (a) False. A rectangle does not have four sides of
equal length.
(b) True
(c) True
(d) False. 36 is not divisible by 14.
2. (a) 1008 – 778 ≠ 18. False because 1008 – 778 = 18.
(b) A cuboid does not have four uniform cross
sections. True
(c) If y = 2x and y = 2x – 1 have the same gradient,
sebenar
then y = 2x is parallel to y = 2x – 1. True
296
(d) If a triangle ABC does not have a right angle at C,
then c2 ≠ a2 + b2. True
(e) If w  5, then w  7. False. When w = 6,
6  5 but 6  7.
Self Practice 3.2a
1.
2.
3.
4.
5.
Deductive argument
Inductive argument
Inductive argument
Deductive argument
Deductive argument
6.
7.
8.
9.
10.
Inductive argument
Inductive argument
Deductive argument
Deductive argument
Inductive argument
Self Practice 3.2b
1. Valid but not sound because premise 1 and conclusion
are not true.
2. Valid and sound
3. Valid and sound
4. Valid but not sound because premise 1 is not true.
5. Not valid but sound because it does not comply with
a valid deductive argument.
6. Valid and sound
7. Not valid and not sound because it does not comply
with a valid deductive argument. A kite also has
perpendicular diagonals but it is not a rhombus.
8. Valid and sound
9. Not valid and not sound because it does not comply
with a valid deductive argument.
10. Valid and sound
Self Practice 3.2c
1. (a)
(b)
(c)
(d)
(e)
(f)
2. (a)
(b)
(c)
(d)
(e)
(f)
Preevena uses digital textbook.
Kai Meng gets a cash prize of RM200.
Quadrilateral PQRS is not a regular polygon.
∆ABC has one axis of symmetry.
m:n=2:3
m + 3  2m – 9
Straight line AB has zero gradient.
All multiples of 9 are divisible by 3.
Polygon P is a nonagon.
If x  6, then x  4.
The room temperature is not lower than 19°C.
If 3x – 8 =16, then x = 8.
Self Practice 3.2d
1. This argument is weak and not cogent because the
conclusion is probably false.
2. This argument is strong and cogent.
3. This argument is weak and not cogent because the
conclusion is probably false.
4. This argument is strong and cogent.
5. This argument is strong but not cogent because
premise 3 is false.
6. This argument is weak and not cogent because the
conclusion is probably false.
Self Practice 3.2e
1. (3n)–1; n = 1, 2, 3, 4, …
n
2. ; n = 1, 2, 3, 4, ...
5
3. 2(n)3 + n; n = 0, 1, 2, 3, ...
4. 20 – 4n; n = 0, 1, 2, 3, ...
Self Practice 3.2f
1. RM43
2. (a) 32 500 residents
(b) 14th year
3. (a) 536 100 – 15 000n (b) 431 100 babies
y
p
sin 40° =
sin 20° =
4. (a) sin 60° =
z
r
y
p
cos 30° =
cos 50° =
cos 70° =
z
r
(b) sin θ = cos (90° – θ)
(c) 0.9848
a
c
a
c
1. (a) A statement because it is true.
(b) Not a statement because the truth value cannot be
determined.
(c) A statement because it is false.
(d) Not a statement because the truth value cannot be
determined.
(e) Not a statement because the truth value cannot be
determined.
(f) A statement because it is true.
(g) Not a statement because the truth value cannot be
determined.
(h) A statement because it is true.
(i) A statement because it is false.
2. (a) True
(b) False. –3 is an integer with negative value.
(c) False. 3 is a fraction larger than one.
2
(d) False. The diagonals of a kite are not
a perpendicular bisector.
3. (a) False
(b) True
(c) True
(d) False
4. (a) All hexagons have 6 vertices.
(b) Some circles have a radius of 18 cm.
(c) Some triangles have three axes of symmetry.
5. (a) (i) Antecedent: p  q
Consequent: q – p  0
(ii) Antecedent: The perimeter of rectangle A is
2(x + y).
Consequent: The area of rectangle A is xy.
(b) (i) x is a multiple of 10 if and only if x is
a multiple of 5.
(ii) 6 is a factor of 12 if and only if 6 is a factor of
24.
(c) (i) If 20% of 30 is 6, then 0.2 × 30 = 6.
If 0.2 × 30 = 6, then 20% of 30 is 6.
(ii) If M is divisible by 20, then M is divisible by
2 and 10.
If M divisible by 2 and 10, then M is divisible
by 20.
6. (a) If α + β = 90°, then α and β are two complementary
angles. True
(b) If w  30, then w  20. False because 28  30
but 28  20.
(c) If p  0, then p2  0. False because –2  0 but
(–2)2  0.
(d) The sum of exterior angles of a poligon is not
360°. False because the sum of exterior angles in
each polygon is 360°.
7. (a) 2 is a factor of 8.
(b) x = 5
(c) If α = β, then sin2 α + cos2 β = 1.
(d) 54 is a multiple of 18.
(e) m  0
(f) The function g(x) is a quadratic function.
8. (a) The surface area of the five similar cones is
700 π cm2.
(b) The equation of the straight line PQ is y = 3x + 5.
9. (a) n2 – 5 ; n = 1, 2, 3, 4, ...
(b) 2n + 3 ; n = 0, 1, 2, 3, ...
(c) 4n + n2 ; n = 1, 2, 3, 4, ...
(d) 3n + 2(n – 1)2 ; n = 1, 2, 3, 4, ..
10. (a) Deductive argument
(b) Inductive argument
11. (a) The pattern of the number of cylinders is 2n +1;
n = 1, 2, 3, 4, ...
(b) 104 720 cm3
12. (a) 32(π + 2), 16(π + 2), 8(π + 2), 4(π + 2)
(c) 1 (π + 2) cm
4
CHAPTER 4 Operations on Sets
Self Practice 4.1a
1. (a) M = {1, 3, 5, 7, 9}
(b) N = {3, 6, 9}
(c) M  N = {3, 9}
2. (a) J  K = {4, 6, 9}
(c) K  L = {9}
3. (a), (b) ξ
P
•3 •17 •19
•7
•2
•11
•13
•5
•15
•10
•20
R
4. (a)
(b)
(c)
(d)
(b) J  L = {3, 9}
(d) J  K  L = {9}
•1
Q
•4
•6
•8
•9
•12
•14
•16
•18
A  B = {I}, n(A  B) = 1
A  C = φ, n(A  C) = 0
B  C = φ, n(B  C) = 0
A  B  C = φ, n(A  B  C) = 0
Saiz sebenar
297
2. (a)
Self Practice 4.1b
R
•28
B
A
C
(A  B)'
4. (a) ξ
B
C
M
N
(A  B  C)'
(b)
ξ P
(c) ξ
Q
J
K
R
(c) 78
Self Practice 4.2c
1.
2.
3.
4.
5.
1. (a) A  B = {b, d, k, n, p, s}
(b) A  C = {f, g, k, l, n, p, s}
(c) B  C = {b, d, f, g, l, n, s}
(d) A  B  C = {b, d, f, g, k, l, n, p, s}
2. (a) ξ
P
Q
x=3
8
11
(a) 25
94
(b) 87
(c) 61
Self Practice 4.3a
1.
M
•55
P
N
•53
•59
R
•50
(b) (i)
(ii)
(iii)
(iv)
3. (a) ξ R
•52
•56
•58
P  Q = {51, 53, 54, 55, 57, 59, 60}
P  R = {51, 53, 54, 57, 59, 60}
Q  R = {51, 53, 55, 57, 59}
P  Q  R = {51, 53, 54, 55, 57, 59, 60}
ξ
(b)
(c) ξ R
R
S
S
T
RT
2. (S  T)  R = {3, 5, 7, 11, 13}
3. (a) P  (Q  R) = {3}
(b) Q  (P  R) = {3, 8}
(c) (Q  R)  P = {2, 3, 6, 7, 8}
S
T
T
RS
4. (a) J  K = {1, 2, 3, 5, 6, 7, 8}
(b) J  L = {1, 2, 3, 4, 5, 6, 9}
(c) J  K  L = {1, 2, 3, 4, 5, 6, 7, 8, 9}
RST
Self Practice 4.3b
1. (a) L'  (M  N) = {13, 15, 19}
(b) (M  N)'  L = {12, 14, 18}
2. 25
3. (a) ξ J
(b) ξ J
K
L
Self Practice 4.2b
1. (a) A' = {3, 4, 7, 8}
(b) B' = {5, 6, 7, 8}
Saiz sebenar
(c) (A  B)' = {7, 8}
298
4. (a) y = 11
(b) 51
L
(J  K  L)'
(Q  R)'
(M  N)'
Self Practice 4.2a
•51
•57
•26
(P  Q  R)'
(b) 30
(b) 15
•54
•60
•22
•20
A
(M  L) = {a, b, c, d, f, g}
(N  L)' = {a, b, c, d, g}
(M  N)' = {a, b, d, f, g}
(L  M  N)' = {a, b, c, d, f, g}
(a) 15
(a) 123
62
16
8
•12
•18
•30
(b) (i) (G  H)' = {15, 20, 22, 24, 26, 28}
(ii) (H  I)' = {11, 13, 15, 17, 19, 20, 22, 26, 28}
(iii) (G  H  I)' = {15, 20, 22, 26, 28}
3. (a) ξ
(b) ξ
Self Practice 4.1c
1.
2.
3.
4.
5.
•10 •21
•14 •25
•16 •27
•23
•29
•15
Q
•24
H
•11
•13
•17
•19
R
(P  R)'
(P  Q)'
4. (a)
(b)
(c)
(d)
I
G
1. (a) (P  Q)' = {2, 4, 6, 8, 9, 10}
(b) (Q  R)' = {3, 4, 5, 6, 7, 8, 9, 10}
(c) (P  Q  R)' = {2, 3, 4, 5, 6, 7, 8, 9, 10}
2. (a) (G  H)' = {11, 12, 14, 16, 17, 18}
(b) (G  I)' = {11, 12, 13, 14, 15, 16, 17, 18}
(c) (H  I)' = {11, 12, 13, 14, 15, 16, 17, 18}
(d) (G  H  I)' = {11, 12, 13, 14, 15, 16, 17, 18}
3. (a) ξ P
(b) ξ P
Q (c) ξ
Q
P
R
ξ
K
L
Self Practice 4.3c
1.
2.
3.
4.
39
x=4
12
(a) 41
(b) 25
(c) 7
1. (a)
(b)
(c)
(d)
2. (a)
(b)
(c)
3. (a)
P  Q = {3, 5}
P  R = {3}
P  Q  R = {3}
(P  Q  R)' = {2, 5, 6}
M  N = {a, b, d, i, k, u}
M  P = {a, b, e, i, k, n, r}
M  N  P = {a, b, d, e, i, k, n, r, u}
P
P
(b)
R
Q
Q
R
PR
PQ
4. (a) T' = {1, 3, 5, 6, 8}
(b) S  T = {2, 4, 5, 6, 7, 8, 9}
(c) S'  T = {2, 4, 9}
(d) (S  T)' = {1, 2, 3, 4, 5, 6, 8, 9}
5. A' = {d, e, f, h, i}
6. (a) Q' = {11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24,
26, 27, 28, 29}
(b) P  R' = {10, 11, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 25, 26, 27, 28, 29, 30}
(c) (P  R)'  Q = {10, 15, 20, 25, 30}
B
7. (a)
(b) A
B
C
C
(b) (i) V = {P, Q, R, S, T, U, V, W}
n(V) = 8
(ii) E = {(Q, P), (Q, R), (Q, W), (R, V), (S, T), (S, U),
(U, V), (V, W)}
n(E) = 8
(iii) 16
(c) (i) V = {A, B, C, D, E, F}
n(V) = 6
(ii) E = {(A, B), (A, F), (B, C), (B, E), (C, D), (C, E),
(D, E), (E, F)}
n(E) = 8
(iii) 16
2. (a) (i) V = {A, B, C, D, E}
n(V) = 5
(ii) E = {(A, B), (A, B), (A, E), (B, C), (B, D),
(B, E), (C, C), (C, D), (D, E), (D, E)}
n(E) = 10
(iii) 20
(b) (i) V = {O, P, Q, R, S, T, U}
n(V) = 7
(ii) E = {(P, U), (P, U), (U, T), (U, T), (P, Q), (P, O),
(Q, R), (Q, R), (Q, O), (R, R), (R, S), (R, S),
(R, O), (S, O), (S, T), (T, O), (U, O)}
n(E) = 17
(iii) 34
(b)
3. (a)
6
8.
9.
10.
11.
12.
13.
39
31
6
(a) 8
(a) 8
50
(b) 11
(b) 5
C  (A  B)'
(c) 54
(c) 7
(d) 2
4
3
P
5
4. (a)
A
A  (B  C)
2
1
(b)
P
Q
S
R
U
(b)
6. (a)
(b)
R
T
S
2
1
5. (a)
Q
5
3
4
CHAPTER 5 Network in Graph Theory
Self Practice 5.1a
1. (a) (i) V = {1, 2, 3, 4, 5}
n(V) = 5
(ii) E = {(1, 2), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4),
(4, 5)}
E = {e1, e2, e3, e4, e5, e6, e7}
n(E) = 7
(iii) 14
Self Practice 5.1b
1. (i) The edges in directed graphs are marked with
direction.
(ii) The order of vertices in directed graphs are
written according to the direction of theSaiz
edges. sebenar
2. A value or information involving edge.
299
P
S
T
3. (a) P
(b)
Q
Q
R
V
U
R
BK
4. (a)
6.6
9.3
(b) 1.6 km
11.4
Self Practice 5.1e
11.6
J
KP
S
B
20.7
40
R
Self Practice 5.1c
1. Subgraph – Diagram 1, Diagram 2, Diagram 3,
Diagram 4, Diagram 8, Diagram 11
Not a subgraph – Diagram 5, Diagram 6, Diagram 7,
Diagram 9, Diagram 10
3. (a) Not a tree
(b) Not a tree
(c) Tree
(d) Not a tree
Q
6. (a)
24
P
R
U
32
20
18
S
30
T
(b) Total weight = 24 + 20 + 32 + 18 + 30
= 124
Self Practice 5.1d
1. (a)
M
KS
5.9
4.9
3. (a)
(b)
K
5.2
M
3.5
T
S
4.9
10
Mervin
Nasi
lemak
Fried
noodles
He
h
iqa
At
Faruk
len
Nurul
Wong
Raj
Ain
Julia
Puspa
rice
Fried rice
(b) Types of food. Each type of food is favoured by
Saiz sebenar
more than two pupils.
300
S
R
T
T
21.9 km
S
U
34.6 km
Kuala Krau
21.1 km
9.3 km
Lanchang Mentakab
Karak
Teriang
CJ
(c) 31.6 km
2. (a) Chicken
R
T
CJ
KS
Q
P
10
15
8
1. (a) (i) V = {P, Q, R, S, T, U}
(ii) E = {(P, Q), (P, S), (P, U), (Q, R), (Q, T), (R, S),
(R, U), (S, T), (T, U)}
(iii) 18
(b) (i) V = {P, Q, R, S, T, U}
(ii) E = {(P, P), (P, Q), (P, R), (Q, R), (R, S),
(S, T), (S, T)}
(iii) 14
(c) (i) V = {P, Q, R, S, T}
(ii) E = {(P, Q), (R, Q), (S, R), (P, S), (S, P),
(S, T), (T, T)}
(iii) 14
P
Q
2. (a)
(b)
5.2
3.5
S
11
1. (a) Johor Bahru – Kuching (Saturday, 0605 hours)
and then Kuching – Miri (Saturday, 1145 hours).
(b) Johor Bahru – Kuching (Friday, 1930 hours)
and then Kuching – Miri (Friday, 2155 hours).
Even though the total price of the flight tickets
is RM35 higher than the cheapest package on
Saturday, Encik Maswi gets to spend more time
with his family.
K
8.4
8
(c) Sum of degrees = Total number of food choices ×
Number of pupils
(d) Graph form
3. (b) Undirected graph. The organisation chart is
a network because it shows the relationships
between the individuals involved based on the
chart’s requirement.
4.9 km
Temerloh
30.2 km
Bandar Bera
(b) Yes, because every pair of vertices is connected
by one edge. Vertex = 7, Edge = 6
4. Route A  C  D  E because it is a safer route even
though Lani had to cycle 300 m more.
5. (a) (i) P  Q  R  S
(ii) P  S
(b) Route P  Q  S because I can save RM35 and
the difference in time is only 9 minutes compared
to route P  S.
6. 11 = x1 + x2,
x4 = x3 + 11,
x2 + x3 = 20,
x1 + 10 = x5,
x5 + 10 = x4,
x1 = 5,
x2 = 6,
x3 = 14,
x4 = 25.
7. (a)
A
3. y = 4x – 5 (3, 7)
F
D
C
E
B
(b) 3.08 km
8. (a) X
●P
●G
●D
●J
●K
y  4x – 5 (2, 4), (–2, 0)
y  –3x + 4 (–1, 8), (–0.5, 7)
y  4x – 5 (0, –6), (4, 5)
y  –3x + 4 (–2, 3), (0, 1)
1. (a)
●B
●C
–2
(ii) 40
(c) 13 068
y
x2
O
2
x
y=x+2
2
x
–2 O
25x + 45y  250 or 5x + 9y  50
2x + 1.5y  500 or 4x + 3y  1 000
0.3x + 0.4y  50 or 3x + 4y  500
1.5x + 3.5y  120 or 3x + 7y  240
(e)
(f)
y
y
–4
y=x
3
1x–2
y  – ­­—
2
yx
x
–2 O
–2
–3
O
3
x
–3
1x–2
y = – ­­—
2
2 –2
y = —x
3
(3, 1)
1
1
(1, –1)
2
(2, –2)
2. (a)
2
y = –x
3 – 2 (1.5, –1)
x
3
2
y  –x
3 – 2 (3, 1), (1, –1)
(1.5, –1)
–2
2.
y
x0
O
2
x
y
–3
(2, 1)
2
4
(1, –2)
6
x
1 +2
Region y  – –x
2
x
O
–3
1 +2
y = – –x
2
(e)
2y < x + 4
x + y = –3
y
(f)
O
1 + 2 (–3, 5),(4, 5)
y  – –x
2
y  –x + 2
2
x
y = –x + 2
x
O
–4
y
2y + x = 2
2
1 + 2 (2, 1)
y = – –x
2
1 + 2 (–3, 1), (1, –2)
y  – –x
2
2
x + y  –3
4
–2
1
(d)
y
(4, 5)
(–3, 5)
O
x
O
1
y = —x
2
2y = x + 4
6
–2
1
y  —x
2
(c)
2
(–3, 1)
y
1 +2
Region y  – –x
2
(b)
y (x = 0)
2 – 2 (2, –2), (3, –2)
y  –x
3
(3, –2)
2 –2
Region y  —x
3
–4
y
yx+2
x
3
(d)
x=2
2 –2
Region y  —x
3
–1
O
–3
(c)
Self Practice 6.1b
O
3
1 +3
y  —x
3
y = –2
y  –2
Self Practice 6.1a
y
y
x
O
CHAPTER 6 Linear Inequalities in
Two Variables
1.
(b)
y
1 +3
y = —x
3
(b) (i) {C, R, K, I}
(ii) {P, G, D, C, R, K, I}
(iii){E}
9. (b) (i) RM1 080
10. (a) third
(b) 484
1. (a)
(b)
(c)
(d)
y = –3x + 4 (1, 1)
Self Practice 6.1c
Y
●A
●L
●E
●T
●R ●N
●F
●H ●M
●I
Z
4.
1
O
2y + x  2
2
x
Saiz sebenar
301
(g)
y
–x + y = –2
(h)
y
–x + y  3
O
x
2
–x + y = 3
3
x
O
–3
–2
–x + y  –2
Self Practice 6.2a
1. (a) x + y  50
(b) x  2y or 2y  x
(c) 8x + 12y  850
2. (a) x + y  500
(b) x  3y or 3y  x
(c) y  200
3. x = green chilli , y = cili padi
(a) x + y  250
(b) x  3y or 3y  x
(c) x  100
(b) A
(b) C
(c) C
(c) A
1. (a) y  x + 4, y  0 and x  0
(b) y  2x – 4, y  –2x – 4 and y  0
(c) 3y  5x, y  x and x  3
2. (a) x  – 4, y  – 1 x and y  0
2
4
(b) y  2x + 4, y  – x + 4 and y  0
3
(c) y  x – 1, y  2 x – 2, x  0 and y  0
3
3. (a) x + y  150, 2y  x
(b)
y (curry puff)
150
50
O
120
y
x=6 y=x
(d)
O
5
y = –5
y=x+2
x=4
1 +2
y = – —x
2
2
O
(c)
3
x (y = 0)
O
–2
(d)
y
x=4
8
4
y
y = –x + 6
y–x=6
80
120
x (floral)
(d)
No. Point (80, 60) is located outside the
shaded region.
x
–5
y
40
(c) 90 m
y=x–5
(b)
y (x = 0)
y = –2x + 6
6
x (y = 0)
3
O
x (y = 0)
6
1
y = —x
3
O
y
y = –x
1 +6
y = – —x
2
x (doughnut)
150
x + y = 120
40
2 +4
y = —x
3
4
O
6
3. (a)
y (x = 0)
x=3
–4
(c)
100
80
x (y = 0)
2
50
(c) (i) 50
(ii) Minimum = 50; maximum = 125
1
4. (a) x + y  120, y  x
3
y (abstract)
(b)
(d) B
(d) D
(c) A
(b)
x + y = 150
O
Self Practice 6.2c
1. (a) C
(b) C
2. (a) y (x = 0) y = 2x – 4
2y = x
100
Self Practice 6.2b
1. (a) D
2. (a) E
Self Practice 6.2d
y=x
x
1. (a)
(b)
(c)
(d)
(e)
(f)
(g)
2y  x + 5, y – x  8
x  0, x  –5
y  4 – x, x  2 – y, y + x  2, y  – 1x
2
y  4, y  –1
y  0, y  10
y  2x – 5, –y  8 – 2x, 2y  x
y  –x – 3, 3y + x  4
(h) 1 y – x  4, 2y  x, –y  4 – x
2
y
y
(b)
2. (a)
4
6
x = –4
2y = 3x
6
Saiz sebenar
302
4
8
y = –2x + 8
x
y = –x + 8
–6
O
x
6 (y = 0)
O
y–x=4
y=4
4
x=4
2
2
O
6
2
4
6
x
–4
–2
O
2
x
(c)
(c) minimum = 10, maximum = 30
(d) RM2 625
8. (a) x + y  1 000, y  1 x
2
y
(b)
y
y = –x
y=2
–2
y=x–4
2
O
2
x
4
–2
(d)(ii)
1 000
–4
750
3. (a) y  –2x, y  x and y  4
1
(b) y  2x, y  2 x and y  – 1 x + 6
2
(c) y – x  4, 2y  x + 4 and y  3
3
(d) y  x + 6, x  – 4, y  5
2
4. (a)
y
1
y = —x
2
250
x + y = 1 000
O
y=x
y = 10
10
O
250
500
750
x
1 000
(c) minimum = 250 m, maximum = 500 m
(d) (i) y  3x
(ii) Refer to the graph.
y + x = 10
CHAPTER 7 Graphs of Motion
x
10
Self Practice 7.1a
(b)
1.
y
6
300
2 +4
y = —x
3
4
x
O
x  3,
(b) y  –2x,
6. (a) y  –1,
(b) x  2,
y  – x,
y0
y  2x – 8, y  – 1x
2
4
x  – 5, y  x – 1
5
y  0,
y  –x + 6
7. (a) x + y  40, y  10,
9
5
10
15
Time
(minutes)
20
3. Time, t (seconds) 0 5
Distance, s (cm)
O
0.2
0.4
0.6
0.8
4. Time, t (minutes)
5 45
Distance, s (km)
1.0
0
1.6
Time
(hours)
8
0
Distance (km)
1.6
40
1.2
30
0.8
20
0.4
10
x  25
O
1
2
3
4
5
Time
(seconds)
O
2
4
6
8
Time
(minutes)
x = 25
x + y = 40
Self Practice 7.1b
20
y = 10
10
10
18
75
50
30
O
27
150
Distance (cm)
y (moden)
40
Distance (km)
36
225
O
–6
5. (a) y  2,
2.
Distance (metres)
45
y=x+6
y = –x
(b)
500
20
30
40
x
(pesak)
1. (a) 50
(b) The car is stationary.
(c) (i) 40
(ii) The car moves for a distance of 100 km with
an average speed of 40 km h–1 in 2.5 hours.
2. (a) 2
(b) 4.8
(c)
Encik Rashid runs for a distance of 4Saiz
km with
sebenar
an average speed of 4.8 km h–1 in 50 minutes.
303
3. (a) 1424
(b) (i) The car is stationary for 66 minutes.
(ii) The car moves with an average speed of
40 km h–1 for a distance of 30 km in
45 minutes.
4. (a) 40
(b) The car moves with an average speed of 54 km h–1
for a distance of 36 km in 40 minutes.
Self Practice 7.1c
1. (a) 3
(b) Yes, Jeffrey will finish the race in 12 seconds.
(b) 70
2. (a) 50
(c)
(d) 11:12 in the morning
Distance (km)
100
Self Practice 7.2c
1. (a) The motorcycle is decelerating at 0.75 m s–2 in
20 seconds; or the speed of the motorcycle
decreases from 35 m s–1 to 20 m s–1 in 20 seconds;
or the motorcycle moves 550 m in 20 seconds.
(b) The motorcycle moves at a uniform speed of
20 m s–1 in 30 seconds; or the motorcycle travels
for 600 m at a uniform speed.
5
2. (a) m s–2
(b) 260 m
6
(c) The particle moves at a uniform speed of 15 m s–1
in 7 seconds.
(b) 1 200 m
3. (a) 3 m s–2
8
(c) Encik Merisat drives for a distance of 1.725 km in
2.5 minutes with an average speed of 41.4 km h–1.
60
Self Practice 7.2d
Time
(minutes)
O
50 70
102
3. (a) 25 minutes
(b) (i) 27
(ii) 33 km
(c) 80
(d) 45
4. (a) 20
(b) 60
(c) The car moves with an average speed of 72 km h–1
for a distance of 36 km in 30 minutes.
Self Practice 7.2a
1. (a)
(b)
Speed (m s–1)
Speed (km min–1)
8
40
6
30
4
20
2
10
O
2
4
Time
(seconds)
6
2. (a) Time, t (seconds) 0 30
O
1
Speed (m s–1)
15
10
20
5
304
0 15
2
Time
(seconds)
3
O
(b) 0.275
1
(b) 29
3
(b) 22.5
(b) 18
(b) 25.5
(b) 15
(c) 14
1. (a) 6 minutes
(b) 60
(c) 42.86
(b) 1.6
(c) 57.14
2. (a) 100
3. (a) 8 seconds
(b) 17
7
(b) 6
(c) 19.68 km h–1
4. (a) –
6
5. (a) 12
(b) 32.4
(c) 60
(b) 0915 hours
6. (a) 80
7. (a) (i) 80
(ii)
Car A moves with an average speed of
25 m s–1 for a distance of 2 km in 80 seconds.
(b) 1 minute
CHAPTER 8 Measures of Dispersion for
Ungrouped Data
Self Practice 8.1a
1 (a) 45, 150
2. p = 30, q = 120
3. 2.3
(b) 105
Self Practice 8.1b
2
4
Self Practice 7.2b
Saiz
Time
(minutes)
Speed (m s–1)
40
1. (a) 360
2
2. (a) 143
sebenar
3. (a) 16
4
Speed, v (m s–1)
60
1
3
(b) Time, t (seconds) 0 5
Speed, v (m s–1) 60 0
O
2
1. (a) 96
2. (a) 1
3. (a) 28
(c) 2.6
6
Time
(seconds)
1.
Group AGroup B
976541
86443220
9887643322100
66532000
64221
4
5
6
7
8
00122689
224566778899
013445699
0025668
2334
In general, the body mass of pupils in group A is
greater than the body mass of pupils in group B.
2.
Self Practice 8.2c
1. (a)
Marks
35
40
45
50
55
60
65
70
April monthly test
25
40
45
50
55
60
65
35
40
45
50
55
60
65
(b)
Marks
35
30
70
May monthly test
The dispersion of May monthly test is smaller.
40
3. (a)
2.
(a) 11
50
(b) 21
(c) 13
60
(d) 18
70
(e) 5 (f) 16
Self Practice 8.2d
6
7
8
9
10
11
12
13
Sizes of shoes for pupils in Class Rose
1.
2.
3.
4.
6, 3.2
9, 29.16
3.742, increased a lot
(a) 2.728
(b) (i) 5.456
(ii) 1.364
5. 100, 43.2
6. 0.9, 1.2
Self Practice 8.2e
1. σA = 0.2506, σB = 0.3706, athlete A is more consistent.
2. σA = 12.65, σB = 6.321, fertiliser B.
6
7
8
9
10
11
12
13
Sizes of shoes for pupils in Class Lotus
(b) The size of shoes for pupils in Class Rose is
dispersed wider compared to Class Lotus.
Class Rose has bigger difference in size of shoes.
Difference in size of shoes for Class Rose
=12.5 – 6 = 6.5
Difference in size of shoes for Class Lotus
=11 – 8.5 = 2.5
Self Practice 8.2a
1.
2.
3.
4.
(a) 7, 3
(a) 5, 2
(a) 7, 2.646
1.26, 1.122
(b) 12, 5.5
(c) 0.9, 0.45
(b) 5, 3
(b) 24.86, 4.986
Self Practice 8.2b
1. Range = 27
Interquartile range = 11
Interquartile range is the most appropriate measure of
dispersion because there is an outlier, 2.
2. Standard deviation, pupil B
3. (a) 2100, 310, 702.2
(b) Interquartile range
Self Practice 8.2f
1. (a)
(b)
2. (a)
(b)
h = 11, k = 18
4.276
∑x = 180, ∑x2 = 1 700
2.25
1. (a) 17, 13 (b) 44, 23
(c) 1.6, 0.75
(d) 20, 5.5
2. (a) 1.2, 0.4
(b) 5, 3
3. (a) variance = 5.917,
standard deviation = 2.432
(b) variance = 52.8,
standard deviation = 7.266
(c) variance = 0.46,
standard deviation = 0.6782
(d) variance = 70.18,
standard deviation = 8.377
4. variance = 130.3, standard deviation = 11.41
5. (a) range = 20, standard deviation = 10.4
(b) range = 2.5, standard deviation = 1.3
6. (a) 360
(b) 16 220
7. (a) (i) m = 7
Saiz sebenar
(ii) 4.980
(b) 223.2
305
8. (a) 90.75
(b) (i) 12 (ii) 9.315
56
9.
3
10. (a) Team A
Team B
mean = 61
mean = 61
range = 22
range = 30
variance = 78.8
variance = 155.6
standard deviation
standard deviation
= 8.877
= 12.47
(b) No because of the existence of outlier or extreme
values
(c) Team B
11. (a) mean = 18, variance = 56
(b) mean = 18.09, variance = 51.02
12. (a) 9, 2, 3.210, 1.792
(b) interquartile range
CHAPTER 9 Probability of Combined
Events
(b) 36
(c) {(1, 2), (1, 3), (1, 5), (3, 2), (3, 3), (3, 5), (5, 2),
1
(5, 3), (5, 5)}; 4
2. {(Y1, Y1), (Y1, Y2), (Y1, Y3), (Y2, Y1), (Y2, Y2),
9
(Y2, Y3), (Y3, Y1), (Y3, Y2), (Y3, Y3)};
64
1
3. {(Y1, Y), (Y2, Y)}; 6
Self Practice 9.2c
1
6
1
{(1, 1), (1, 3), (3, 1), (3, 3)};
4
0.2025
3
{(C, E), (C, I), (L, E), (L, I), (K, E), (K, I)};
10
B = Burnt bulb
B' = Not burnt bulb
1. {(A, 2), (U, 2)};
2.
3.
4.
5.
1
—
11
2
—
12
Self Practice 9.1a
1. {(H1, H2), (H1, G), (H1, M), (H2, H1), (H2, G), (H2, M),
(G, H1), (G, H2), (G, M), (M, H1), (M, H2), (M, G)}
2. {(B, B), (B, G), (G, B), (G, G)}
3. {(1, T), (2, T), (3, T), (4, T), (5, T), (6, T), (1, H),
(2, H), (3, H), (4, H), (5, H), (6, H)}
4. {AAA, KKK, AAKA, AKAA, KAAA, KKAK,
KAKK, AKKK, KAKAA, KAAKA, KKAAA,
AAKKA, AKAKA, AKKAA, AAKKK, AKAKK,
AKKAK, KAAKK, KAKAK, KKAAK}
Self Practice 9.2a
1.
2.
3.
4.
5.
Self Practice 9.2b
Saiz sebenar
306
First
dice
B'
1
—
66
6. (a) 0.3166
10
—
11
2
—
11
B'
9
—
11
B'
B
(b) 0.2108
Self Practice 9.3a
1. (a)
(b)
(c)
2. (a)
(b)
(c)
3. (a)
(b)
(c)
Independent events
Dependent events
Independent events
Dependent events
Independent events
1. (a)
10
—
12
B
B
Non-mutually exclusive events
Mutually exclusive events
Non-mutually exclusive events
Non-mutually exclusive events
Non-mutually exclusive events
Mutually exclusive events
Mutually exclusive events
Non-mutually exclusive events
Non-mutually exclusive events
Second dice
1
2
3
4
5
6
1
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
Self Practice 9.3b
1. (a) {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6),
(1, 5), (2, 5), (3, 5), (4, 5), (5, 1), (5, 2), (5, 3),
7
(5, 4)}; 18
(b) {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6), (1, 1),
5
(2, 2), (3, 3), (4, 4)}; 18
(c) {(1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (5, 1),
(5, 2), (5, 3), (5, 4), (5, 6), (1, 1), (2, 2), (3, 3),
4
(4, 4), (6, 6)};
9
2. (a) {TT, HH}; 1
2
3. (a) (91, R), (77, I), (77, A), (91, A)
(b) (i) {(77, R)}, 1
6
(b) {TT, TH, HT}; 3
4
(c) {HH, TH, HT, TT}; 1
3. (a)
ξ
L
•H •G
•A •A
•I •A
N
(ii) {(77, R), (77, I), (77, A), (91, R)}, 2
3
M
4.
3
—
5
•B
F4
(b) (i) {B, A, H, A, G, I, A}; 1
(ii) {A, A, A, I, B}; 5
7
(iii) {B, H, G}; 3
7
Self Practice 9.3c
1. {E, I, A, R}, 4
7
2. {(S, 4), (S, 5), (S, 6), (E, 6), (R, 6), (I, 6)}, 1
2
3. ξ
J
K
7
—
24
4.
4
—
7
3
—
7
47
—
98
1
—
12
9
—
14
M
M'
5
—
36
35
—
72
; 35
72
G
5
—
14
9
—
14
G'
5
—
14
G'
G
Self Practice 9.4a
1. 12 000
2. 13
36
3. Pantai Cengal, because the probability of not raining
on both days at Pantai Cengal is higher.
4. 230
2
—
5
F5
2
—
4
F4
2
—
4
F5
3
—
4
F4
1
—
4
F5
2
5
5. (a) 0.2436
(b) 0.5128
6. (a) 199
540
(b) 47
54
7. (a) 2
3
(b) 4
9
8. (a) (i) 25
156
(ii)
211
468
(b) RM70
9.
43
200
7
10. (a) 33
(b) 5
33
11. (a) (i) 0.191
(ii) 0.784
(b) Not advisable. Love your life
CHAPTER 10 Consumer Mathematics:
Financial Management
1. {(B1, B2), (B1, B3), (B1, G1), (B1, G2), (B2, B1), (B2, B3),
(B2, G2), (G1, B1), (G1, B2), (G1, B3), (B2, G1), (B3, B1),
(B3, B2), (B3, G1), (B3, G2), (G1, G2), (G2, G1), (G2, B1),
(G2, B2), (G2, B3)}
2. (a) 1
15
(b) 7
30
Self Practice 10.1a
1. Financial management is a process that involves
managing money from sources of income into
savings, expenses, protection and investment.
2. The financial management process consists of setting
goals, evaluating financial status, creating a financial
plan, carrying out the financial plan, and reviewing
Saiz sebenar
and revising the progress.
307
3. Setting a financial goal will affect the total monthly
savings in achieving the goal.
4. Short-term financial goals are less than a year and do
not involve a large amount of money to be achieved.
Long-term financial goals are more than five years
and involve a large amount of money as compared to
the short-term financial goals.
5. Puan Salmah has been practising the financial goal
setting based on the SMART concept which is specific
– she needs to save an amount of RM3 000 to buy
a laptop, with monthly savings of RM300 and this
goal is not difficult to be achieved with the total
income earned as well as it is realistic with a saving of
RM300 for 10 months (time-bound).
Self Practice 10.1b
1. • Inflation
• Government policy
• Personal health
2. (a) Mrs Thong does not spend wisely because her
total monthly savings of RM250 compared to the
income of RM6 000 which is less than 10%.
(b) Mrs Thong will not be able to achieve the
investment goal of RM500 000 with monthly
savings of RM250.
7. We should start to cultivate the saving habit as early as
possible to ensure that financial goals can be achieved
as planned.
8. (a) Personal monthly financial plan for Encik Nabil
Income and Expenditure
Active income:
Net salary
Commissions
RM
3 800
450
4 250
Total active income
Passive income:
House rental
600
Total passive income
600
Total monthly income
Minus fixed monthly savings
4 850
380
Total income after deducting
savings
Minus cash outflow/expenses
Fixed expenses:
Housing loan instalments (1)
Housing loan instalments (2)
Insurance expenses
4 470
800
500
350
Total fixed expenses
1. Do not prepare for financial planning, not spending
wisely, uncontrolled use of credit cards, failure to pay
off the loans and car instalments.
2. Negative cash flow of an individual in a financial plan
will lead to the individual’s bankruptcy and he or she
will not have enough savings in case of emergency.
3. A financial plan is created with the aim of estimating
the initial budget to achieve goals and monthly
savings that are needed to achieve short-term goals
and long-term goals, analyse spending behaviour as
well as setting a duration to achieve the goals.
4. When we review and revise the progress of
a financial plan, it gives us some space to refine our
nature of spending and it also helps in generating
more income in order to achieve the goals.
5. Inflation, changes in government taxation policies,
economic policies and others.
6. The way of spending can be adjusted based on financial
goals. Actions can be taken such as generating more
income.
Saiz sebenar
308
Variable expenses:
Food expenses
Utility payments
Toll and petrol expenses
Internet service subscription
Eat at a luxury restaurant
1 650
900
150
200
100
400
Total variable expenses
1 750
Surplus/Deficit
1 070
(b) Encik Nabil’s personal financial plan has a surplus
where there is a positive cash flow when the total
income is more than the total expenses. This has
improved Encik Nabil’s liquidity.
9. (a) Positive cash flow – enables savings and achieves
goals as planned.
(b) Negative cash flow – making it difficult for
someone to achieve financial goals and more
inclined to obtain loan resources such as credit
cards.
Glossary
Argument (Hujah)
A set of statements called the premises and
a conclusion.
Bankrupt (Bankrap)
A situation where a person is unable to settle
his/her debts because his/her expenses exceed
income. As a result, the court declares the
person a bankrupt.
Combined events (Peristiwa bergabung)
An event formed from the union or intersection
of two or more events.
Deceleration (Nyahpecutan)
A negative acceleration.
Deductive argument (Hujah deduktif)
A process of making a special conclusion based
on general premises.
Degree (Darjah)
The number of edges that connect two vertices.
Digit (Digit)
The symbols used or combined to form
numbers in the numbering system. 0, 1, 2, 3,
4, 5, 6, 8, 9 are 10 digits used in the decimal
number system. For example, number 124 651
has six digits.
Directed graph (Graf terarah)
A graph in which a direction is assigned to the
edge connecting two vertices.
Discrete (Diskret)
The countable values.
Displacement (Sesaran)
The vector distance from a fixed point is
measured in a certain direction.
Distance (Jarak)
The length of the space between two points.
Distance-time graph (Graf jarak-masa)
A graph that shows the distance travelled per
unit of time. The gradient of the graph shows
the speed measured.
Edge (Tepi)
A line that connects two vertices.
Graph (Graf)
A series of dots that are linked to each other
through a line.
Inductive argument (Hujah induktif)
A process of making a general conclusion based
on specific cases.
Inflation (Inflasi)
Situation of a continuing increase in the general
price level.
Intersection of sets (Persilangan set)
A set that contains the common elements of
two or more sets. The intersection is illustrated
with the symbol .
Inverse (Songsangan)
An inverse of an implication “If p, then q” is
“If ∼p, then ∼q”.
Linear (Linear)
A description of something that is related to or
in the form of a straight line.
Linear inequalities (Ketaksamaan linear)
The inequalities that involve linear expressions
such as y  mx + c, y  mx + c, y  mx + c,
y  mx + c where m ≠ 0, x and y are variables.
Linear inequality system
(Sistem ketaksamaan linear)
A combination of two or more linear
inequalities.
Loop (Gelung)
An edge that is in the form of an arc that starts
and ends at the same vertex.
Mutually exclusive events (Peristiwa saling
eksklusif)
If two events, A and B, do not intersect with
each other, then event A and B are said to be
Saiz sebenar
mutually exclusive.
309
Network (Rangkaian)
Part of a graph with vertices and edges.
Number bases (Asas nombor)
Numbering system of a number.
Place value (Nilai tempat)
The value of a digit on the basis of its position
in a number. For example, the place value of
digit 6 in 6 934 is thousands and the place value
of digit 5 in 523 089 is hundred thousands.
Premise (Premis)
A statement that is assumed (considered) as
something that is true for the purpose of making
a conclusion later.
Probability of independent events
(Kebarangkalian peristiwa tak bersandar)
Two events, A and B, are said to be independent
if the probability of event A does not affect the
probability of event B.
Speed-time graph (Graf laju-masa)
A graph that shows the relationship between
the speed of an object in a certain period of
time. The gradient of the graph represents
acceleration. The area under the graph shows
the total distance travelled.
Standard deviation (Sisihan piawai)
A statistical measure that measures the
dispersion of a set of data.
Statement (Pernyataan)
A sentence that the truth value can be
determined.
Subgraph (Subgraf)
Part of a graph or the whole graph redrawn
without changing the original positions of the
vertices and edges.
Tree (Pokok)
A subgraph of a graph that has minimum
connection between vertices without loops and
multiple edges.
Quadratic equation (Persamaan kuadratik)
An equation that can be written in the general form
ax² + bx + c = 0 where a, b and c are constants
and a ≠ 0. This equation has one variable and the
highest power of the variable is 2.
Uniform speed (Laju seragam)
The distance that constantly increases with time.
Quadratic function (Fungsi kuadratik)
A function in the form of f (x) = ax2 + bx + c
where a, b, c are constants and a ≠ 0. The
highest power of the variable is 2 and has only
one variable.
Unweighted graph (Graf tak berpemberat)
The edges that connect two vertices of a graph
is not stated with weighted values such as
distance, cost, time and others.
Region (Rantau)
An area that satisfies a system of linear
inequalities.
Simple graph (Graf mudah)
An undirected graph without loops or multiple
edges.
Speed (Laju)
The rate of change in distance.
Saiz sebenar
310
Union of sets (Kesatuan set)
A combination of all the elements of two or
more sets. Its symbol is .
Variable (Pemboleh ubah)
A quantity with a varied value and is represented
by symbols such as x, y and z that can take any
values from a particular set of values.
Vertex (Bucu)
The dot where the edge is connected to.
Weighted graph (Graf pemberat)
The edges that connect two vertices of a graph
is stated with weighted values such as distance,
cost, time and others.
References
Bondy, J.A. and Murty, U.S.R. (1982) Graph Theory With Applications. New York. Elsevier
Science Publishing Co. Inc.
Christopher, C. (1991). The Concise Oxford Dictionary of Mathematics. Oxford University Press.
Glosari Matematik Pusat Rujukan Persuratan Melayu, Dewan Bahasa dan Pustaka is referred to the
website http://prpmv1.dbp.gov.my
Izham Shafie. (2000). Pengantar Statistik. Penerbit Universiti Utara Malaysia.
James, N. (2008). A Level Mathematics for Edexcel Statistics S1. Oxford University Press.
Lan, F. H. and Yong, K. C. (2016). Revision Essential Additional Mathematics SPM. Sasbadi
Sdn. Bhd.
Mok, S.S. (2011). Logik dan Matematik Untuk Penyelesaian Masalah. Penerbitan Multimedia
Sdn. Bhd.
Murdoch, J. and Barnes, J.A. (1973). Statistik: Masalah dan Penyelesaian. Unit Penerbitan
Akademik Universiti Teknologi Malaysia.
Nguyen-Huu-Bong. (1996). Logik dan Penggunaannya untuk Sains Komputer. Penerbit Universiti
Sains Malaysia.
Ooi, S.H., Moy, W.G., Wong, T.S. and Jamilah Binti Osman. (2005). Additional Mathematics
Form 4. Penerbit Nur Niaga Sdn. Bhd
Paul, Z. (1999). The Art and Craft of Problem Solving. John Wiley and Sons, Inc.
Ted, S. (2018). Mathematical Reasoning: Writing and Proof. Pearson Education, Inc.
Terlochan, S. (1986). Buku Rujukan dan Kamus Matematik. Kuala Lumpur, Malaysia. Tropical
Press Sdn. Bhd.
Wan Fauzi Wan Mamat. (2010) Probability. Visual Print Sdn. Bhd.
Wong, T.S., Moy, W.G., Ooi, S.H., Khoo, C., and Yong, K.Y. (2005). SPM Focus U Matematik
Tambahan. Penerbitan Pelangi Sdn. Bhd.
Yap, B. W. and Nooreha Husain. (1998). Pengenalan Teori Kebarangkalian. IBS Buku Sdn. Bhd.
Saiz sebenar
311
Index
Acceleration 195, 200, 203
Active income 274, 276
Antecedent 63, 64, 68
Argument 71, 72, 75
Assets 274
Attainable 273, 274, 283
Average speed 189, 197, 203
Axis of symmetry 8, 9, 12
Bankruptcy 289
Box plot 226, 227, 230
Cash flow 274, 276, 282
Coefficient 4
Combined events 244, 246
Common region 169, 174
Complement 100, 110
Compound statement 60, 89
Conclusion 71, 73, 75
Consequent 63, 64, 68
Constant 3, 23
Contrapositive 66, 67, 68
Converse 66, 67, 68
Counter-example 69, 70
Cumulative frequency 221
Dashed line 158, 162, 171
Deceleration 200, 202
Deductive 71, 73, 75
Degree 131, 133, 136
Dependent events 246, 247
Digit value 36, 37, 39
Directed graph 135, 136
Dispersion 212, 213, 217
Distance 184, 197
Distance-time graph 184, 197
Dot plot 213, 215, 217
Edge 130, 132, 135
Expenses 272, 273, 274
Expression 2, 3, 16
Extreme value 224, 228
Factorisation 21, 23
Financial goal 272, 273, 274,
Saiz sebenar
275, 282
312
Financial plan 272, 274, 277
Financial planning 272, 273,
277, 279
Fixed expenses 274, 278, 282
Frequency table 212, 219, 221
Graph 130, 135, 139
Implication 63, 66, 68
Independent events 246, 249
Inductive 72, 73, 81
Inflation 284, 285, 288
Interquartile range 212, 219,
220
Intersection of sets 96, 100
Inverse 66, 67, 68
Liabilities 274
Linear inequality 156, 158
Linear inequality system 167
Long-term 272, 274, 275, 282
Loop 132, 136
Maximum point 7, 8, 9
Measurable 273, 283
Median 220, 226, 227
Minimum point 7, 8, 9
Multiple edges 131, 132
Mutually exclusive events 253
Needs 273, 280
Negation 59, 70
Network 130, 143
Non-mutually exclusive events
253, 255, 259
Number base 34, 45
Observation 213
Outlier 224, 229
Passive income 274, 276, 287
Place value 35, 36, 39
Premise 71, 72, 81
Quadratic 2, 3, 7, 9
Quadratic equation 15, 16, 21
Quadratic function 2, 5, 7, 9
Range 212, 219, 224
Rate of change in distance with
respect to time 184, 189, 191
Rate of change of speed with
respect to time 195, 200, 201
Realistic 273, 274, 283
Region 158
Root 16, 17, 18, 22
Sample space 244, 245
Short-term 272, 274, 282, 285
Simple graph 131, 134, 139
SMART 273, 279, 280, 283
Solid line 158
Specific 273, 277, 283
Speed 184, 187, 189
Speed-time graph 195, 197
Standard deviation 212, 221,
224
Statement 56, 58, 59, 60
Stationary 187, 194
Stem-and-leaf plot 214, 216
Subgraph 139
Time 184, 195
Time-bound 273, 274, 283
Tree 139, 146
Truth value 56, 57, 59
Undirected graph 135, 143
Ungrouped data 219, 220
Uniform speed 187, 200
Union of sets 106, 110
Unweighted graph 137, 143
Validity 75
Variable 2, 3, 16, 156
Variable expenses 274, 278
Variance 221, 228, 229
Vertex 130, 132, 139
Wants 273
Weighted graph 137, 143
SKIM PINJAMAN BUKU TEKS
Sekolah
Tahun
Tingkatan
Nama Penerima
Nombor Perolehan:
Tarikh Penerimaan:
BUKU INI TIDAK BOLEH DIJUAL
Tarikh
Terima
DUAL LANGUAGE PROGRAMME
MATHEMATICS
FORM
ISBN 978-983-77-1531-8
FORM